What Are Variables For?Date: 02/09/2001 at 04:54:54 From: Cindy Subject: Variables Hi! I just wanted to ask, why is it important to be able to figure out the values of variables? We've been doing that in our math class for more than half a year and I was just wondering. Cindy Date: 02/09/2001 at 13:24:58 From: Doctor Ian Subject: Re: Variables Hi Cindy, This is a very perceptive question. Variables are important for a couple of reasons, which we might call 'planning' and 'analysis'. Think about planning a dinner party. You know that you'll need one half of a chicken for each adult, and one quarter of a chicken for each child; you'll need one bottle of wine for every three adults, and one bottle of soda for every five children; you'll need a half pound of potatos for each chicken that you have to cook; you'll need one pie for each six adults, and one bowl of jello for each child; and so on. But you don't yet know how many people you're going to invite. Variables let you set up a description of the situation (i.e., an equation) such that you can plug in two numbers (the number of adults, and the number of children) and get back other numbers that you'll find useful: how many chickens to buy, how much the total cost will be, and so on. If you decide at the last minute that you want to add another three guests, you don't have to start your calculations from scratch - you just change the values coming in, and the equations will tell you how to change the values at the other end. This, by the way, is why they are called 'variables' - they tell you how some quantities vary in response to changes in other quantities. Note that a dinner party isn't all that complicated, so it's almost not worth the effort of setting up equations to solve the problems. The same is true of a lot of the problems that you'd see in a math class, which is one of the things that can make math (as it's taught in schools) seem kind of pointless. But when you get to something more complicated - like trying to plan a flight, or run an entire airline - it becomes absolutely necessary to make use of the kinds of techniques that you learn in your math classes. A big part of running any business is being able to figure out your potential costs in any situation, because that tells you how much you need to charge for goods and services in order to make enough money to stay in business. So, that's planning. What about analysis? Well, analysis is just planning in reverse. If you know how many people to invite, you can figure out how much money you'll have to spend. That's planning. If you know how much money you spent, you can figure out how many people you invited. That's analysis. The beauty of variables is that in most cases, you can use the same equations to go in either direction - to predict what's going to happen, or to understand what already happened. The planning aspect tends to be more useful in things like business, or construction, or engineering, where you have to decide what's going to happen. The analysis aspect tends to be more useful in science, where you don't get to decide what happens (the world behaves the way it behaves, whether you like it or not), but would like to understand it anyway, whether just from curiosity, or because you'd like to use that understanding to make your planning more accurate. I hope this helps. Please write back if you'd like to talk about this more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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